用近似留一法加速置信预测，计算更快且结果更准。
Accelerating Conformal Prediction via Approximate Leave-One-Out
- 引入近似留一法估算模型残差，大幅减少重训练次数。
- 理论证明覆盖概率接近精确方法，效率损失极小。
- 适合需要快速不确定性估计的高维数据场景。
置信预测虽能通用量化预测不确定性，但常因计算成本过高受限。现有方法如Jackknife+和Jackknife-minmax通过牺牲少量效率实现加速，但仍需对所有样本进行留一重训练。本文进一步利用近似留一法（ALO）估算器加速置信预测，并建立渐近覆盖性和效率性。尽管证明借鉴了高维统计中用于分析ALO交叉验证风险估计一致性的方法，但需针对置信预测进行调整——因需在新点$ x_{n+1} $处计算留-$ i $-out残差，而非仅在训练点$ x_i $。模拟结果验证理论：基于ALO的方法在覆盖率和效率上接近精确方法，同时显著降低运行时间。
原文摘要 · Abstract (English)
While conformal prediction provides a general framework for uncertainty quantification in predictive inference, its application is often limited by computational cost. Recent methods, including Jackknife+ and Jackknife-minmax, achieve faster computation by trading a slight loss of efficiency relative to full conformal prediction, but still requires computing leave-one-out refits for all observations. In this paper, we further accelerate conformal prediction by incorporating approximate leave-one-out (ALO) estimators, and establish asymptotic coverage and efficiency. While our proof draws on methods developed for analyzing the consistency of ALO cross-validation risk estimators in high-dimensional statistics, it requires adaptations to handle conformal prediction, where leave-$i$-out residuals are needed for predictions at $x_{n+1}$ rather than just at the training covariate $x_i$. Simulation results validate our theoretical findings, showing that the ALO-based methods achieve coverage and efficiency comparable to the exact methods, while significantly reducing the runtime.
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